Question 2: How to study calculus? You only studied analytic geometry in high school, and you didn't have enough foundation. You should know algebra in high school! You don't need to be too proficient, just know what algebraic formulas are, such as trigonometric functions. Besides, I don't know how your computing ability is. Mathematics problems in senior high school require higher computing power than those in junior high school, and at least factorization and some transformations are much more flexible.
Both the derivation of calculus and the calculation of definite integral need calculation skills. Calculus is not like elementary mathematics. Understanding is the most important thing. If you don't know what calculus is, you can't start by telling you some words in the formula.
Actually, I don't think calculus has much to do with high school stuff. You only need to have a little impression of high school mathematics, but trigonometric functions, logarithms, exponents, and Pythagorean theorem should also be known. The rest is the calculation skills, skills are practiced. If you can do tens of thousands of calculus problems, you don't have to worry about skills. Calculus needs to do more problems.
If you buy books, you should buy some basics. At present, the routines of ordinary calculus textbooks are the review of basic knowledge of functions, such as limits, derivatives, differentiation, derivative applications, mean value theorem, max-min problems, indefinite integrals and definite integrals. In-depth textbooks also bring some Taylor series, vectors, double triple integrals and so on.
Just visit the bookstore according to your own taste. What I recommend to you may not be suitable for you.
Question 3: How to learn calculus well has nothing to do with high school. After thoroughly understanding extreme thoughts, the remaining calculus is based on the system of extreme thoughts, that is, some methods and techniques. Basically, relying on extreme value theory, directly learning how to calculate integrals or do proof problems is to give up the foundation.
Question 4: How to learn calculus well 1: Pay attention to the concept and master the origin of each formula theorem. These deduction methods are also ideas for doing the problem.
Calculus is a tool, and it needs to be used well to learn calculus well. For example, in some problems of physics or mathematics. Try to think about whether you can answer it with calculus.
2. Find ways to eliminate the fear of mathematics, find some interesting math topics, build confidence and come back to study calculus. When learning, we should focus on the origin and deduction of calculus formulas, which is much better than simply memorizing formulas. And some problems are solved by the definition of calculus, without calculus formula.
3. Our teacher held out two fingers in class and said, "Learn calculus well and do more exercises."
4. The origin of all concepts of calculus is limit, and the proposal of limit depends on.
A set of mathematical languages is called ε-δ. Therefore, the key to learn calculus well is to master this analytical language (this is a mathematics major). If you can't understand the explanation in the book, don't force the problem, first find a book on calculus or the history of mathematics. The purpose of reading such books is to deeply understand the background of the concept of calculus and understand the evolution of mathematics thoughts at that time (of course, this will also become the evolution of your thoughts). Do this step well and you will understand what the limit is. What is differential? Wait a minute. Then you can study your textbook, supplemented by quantitative exercises. Remember, this is a matter of consolidating understanding, not dealing with those boring exams. If you do this step well, then you will have a deeper understanding of the concept of calculus. At this time, you may be interested in calculus. Of course, you can study further. You can do more questions if you want to cope with the exam. For example, do the classic Jimidovich mathematical analysis problem set (of course, it is optional, not all). Now you are a quasi-master. However, you need further training and reading.
5. First understand the function and actual situation of calculus, memorize the basic formula, have the concept of model in your mind, and it is best to understand the original method of calculus.
6. Math training logical thinking! This is very important. The ability of logical thinking, whether innate or acquired, can certainly be cultivated, and one of the ways is through learning mathematics. Solving mathematical problems will teach you how to approach problems, learn how to see the key of problems, ask appropriate questions, think about problems from different angles and so on. The ability of logical thinking is much more useful than mathematics, such as learning a new language, organizing and planning.
In a word, every student should and can find the motivation to learn calculus. You don't have to agree that calculus is one of the greatest achievements of mankind. The beauty of this theory is dazzling. But at least calculus is regarded as an important tool to master the subject, and it is also an important theory to teach you how to systematically attack and solve problems.
Question 5: How to learn calculus well?
1. Calculus in advanced mathematics (taking number one as an example) can be roughly divided into one-dimensional calculus and multivariate calculus. The difference between them is not only the number of independent variables, but the difference between two dimensions (plane) and n dimensions; This difference is very abstract, and it is by no means the difference between "tangent line" and "tangent plane of surface" in existing textbooks. Therefore, from this aspect, first understand and understand the nature and difficulty of N-element calculus, in order to better learn advanced calculus;
2. The essence of calculus is actually: △ x; When △x approaches a certain value, such as △x→0, the case of studying the dependent variable of the function is differential (similarly, the concept of continuity can be obtained); When the value of △x is in a certain domain (* * *), the case of studying the dependent variable of the function is integration. Multiple calculus is similar. The trouble is whether △x and △y approach at the same time. If so, what is the change of z (suppose the function here is: z=z(x, y))? If not, what about the change of z when △x and △y approach respectively? When it changes alone, it is the partial derivative, that is:? z/？ X or? z/？ Y. Similarly, if the linear consistency of △x and △y approaches * * * d (the * * * isomorphic space of x and y), then it is a double integral; And if the upper or lower limit of *** D approximated by △x and △y is ∞, then it is a generalized integral.
3. To sum up: the essence of calculus is: when the independent variable approaches a certain value, it approaches a certain * * *, the change or value of the dependent variable!
The definitions of 4 and 3 are essentially different from those in current books. Using tangent to explain the definition of books obliterates the abstract essence of calculus. The result derivative is tangent or tangent plane, which is obviously a narrow understanding.
5. Therefore, to learn calculus well, we must first firmly grasp the abstract essence of calculus, that is, "extreme division thinking" or "extreme approximation" thinking; Furthermore, we should keep in mind the properties and definitions of some elementary functions, such as quadratic function (or polynomial function), trigonometric function, exponential/logarithmic function and so on. Only by understanding the characteristics of these functions can we better understand its calculus.
6. Finally, no matter what the essence of calculus is, it is aimed at functions, which is actually a special kind of * * *. Therefore, learning calculus well requires a deep understanding of the concept and nature of * * *.
Question 6: How can we learn calculus quickly and effectively? Calculus is a branch of mathematics, which studies the differential and integral of functions and related concepts and applications in higher mathematics. It is a basic subject of mathematics, which not only runs through mathematics from beginning to end, but also has a wide range of applications in other disciplines. We must study hard!
1, preview before class, and take notes if you don't understand.
2. Listen carefully in class and focus on what you don't understand in preview.
Do more exercises after class and ask the teacher in time if you don't understand.
4. When learning calculus, don't buy a lot of reference books and read them mindlessly. Be sure to choose a good one to complete the exercises, understand the problems that you can't, and pay attention to communicating with teachers and classmates.
5, pay attention to doing the problem, not looking at the problem, understanding does not mean that you can do it, the focus of training is thinking and methods.
Question 7: How to learn calculus quickly? First of all, according to the teacher's requirements, complete the teacher's tasks in class and after class with high quality. This is the first stage. What the teacher explains in detail should be calculated carefully, such as the proof of Lagrange mean value theorem and Stokes integral formula. If the teacher doesn't explain the ins and outs of a theorem in detail, then put it aside and enter the second stage.
Because if the content of a math textbook is calculated by 100%, the teacher may only involve 15%-20% in class, so the teacher will skip many theorem proofs and even some important chapters will not be involved in the final exam. If you get caught up in it, it will definitely delay time and progress, leading to poor final results.
Doing a lot of exercises is not recommended at this stage. Finish the exercises assigned by the teacher, and add a little exercise at most. Mastering what the teacher wants to teach you in class is the basis of learning. The exam score is not important, so I went to do some exercises that I thought were important. This is a mistake I made in the past. Since I think the exam is simple, why not do it well?
There are two conditions for entering the second stage. First, there is spare capacity for learning; Second, you should do well in math. It is wrong to rush to do more advanced content before the basic things are done. It is wrong to start the second stage after completing the first stage task.
In the second stage, we should broaden our horizons. At this time, we need to do a lot of problems to understand the basic abstract concepts of mathematics and find some good teaching materials and problem sets. Fichkingolz of the former Soviet Union has a set of six books >: the content is solid and the topic is challenging, which is a set of exercises laid by many Daniel. The content is also very solid, and richard courant's >; . The follow-up of mathematical analysis includes complex variable function analysis and real analysis, which you should not touch, but mathematics majors attach great importance to it, and real analysis is difficult. Some schools are only for graduate students. Don't worry about the future, try to do well in the present. Finally, if you want to develop in mathematics, you should go to a more professional place, not just a general hobby.
Question 8: How to study calculus? 5 points 1. The study of calculus is really different from that of high school mathematics, and the mathematical ideas involved are much deeper than that of high school.
Even college graduates, most of them have studied calculus, but most of them have not.
Understand the ideas and methods of calculus. So, just find a college graduate, especially a graduate.
A few years later, people who are not engaged in teaching or theoretical research ask a simple calculus question. They at least have
More than 90% will definitely say "I studied for a long time and forgot". This shows that they didn't learn well at all.
I don't understand at all. As long as you have learned it from the beginning, you will not forget the truth, and the problem will not be solved and understandable; simple
None of the questions, 100%, are memorized, memorized and swallowed. These people who have studied calculus, in
Old farmers are boastful capital, a disgrace to their children and a permanent pain in their work.
If the landlord wants to be outstanding and not follow the footsteps of most college graduates, he should:
1, you'd better learn by yourself or preview first. This sentence is easier said than done.
Specifically, what do you mean by trying to understand every definition, every formula and every method?
Why? What exactly does this mean?
2. Usually we say that learning with questions, the higher level is to learn with your own understanding and your own predictions.
In other words, you not only have questions you don't understand, but also have your own predicted answers. Or, after reading the last chapter,
Generally, I can predict what will be said in the next chapter. It's hard to say, it's easier said than done. if
When you can roughly predict what you will say in the next chapter, your confidence will increase unprecedentedly, and you will feel that you have
Predictive ability, over time, self-study ability is cultivated. What ordinary people call "self-learning ability" is made up of
Less than this state, their "self-study ability" is only the ability of rote memorization and gang-wearing.
If you have this highest level of "self-study ability", you already have the ability to "write books and make presentations".
Don't be limited by the concept of middle school. Some concepts in middle school are wrong, and some are right under special circumstances.
Middle school knowledge is only a special case. After entering the world of calculus, it gradually enters the general situation.
For example, 0 can't be the denominator, nor can universities, but many students say that the limit of 0/0 type violates mathematical principles.
This is just what a half-baked classmate said. Another example is that the zeroth degree of any number is 1, so many students don't.
Method to understand the limit process of 0 to the power of 0. For another example, the limit that any power of 1 is an infinite power of 1 and 1 is even more.
It's hard to understand.
4. The concept is understood and will be summarized immediately; Then solve more problems and raise awareness through a large number of problems. Study hard.
Most integrated people are unwilling to solve more problems, thinking that solving a few is enough. In fact, I can't understand thousands of questions.
There can be no real understanding! After solving the problem, you should summarize the problem, summarize the method, summarize the problem, and then
Forecast, confirm, forecast,,,. Over time, the master was born. Come on!
The hardest thing is not to be misled by some teachers. For example, equivalent infinitesimal substitution is rendered as having in China.
Teachers and professors are a dime a dozen. In fact, looking at the international situation, it is not so ridiculous. As a student, the only one
The way is to read more international textbooks.
Good luck with your study!
Welcome questions.
I hope I can solve your problem.
Question 9: Is calculus difficult to learn? . . ? How to learn calculus well
The difference between elementary mathematics and advanced mathematics. Elementary mathematics mainly studies discrete quantities, but it is high
Isomathematics is a continuous quantity. Because of this, advanced mathematics is difficult to learn. Here, and
Calculus in advanced mathematics is the basis of other mathematical knowledge, so we study differential calculus in combination with many colleges and universities.
In this article, I will talk about the methods of calculus learning.
First of all, we must affirm the greatness of calculus. The creation of calculus is not so much mathematics.
In history, this is a great event in human history. Today, it is very important for engineering technology.
Just as telescopes are as important to astronomy and microscopes are to biology. Its appearance is not
Not coincidentally, it has a long growing process. As early as ancient Greece, Archimedes and others
His works already contain the seeds of integral calculus. After more than a thousand years of silence, Europe appeared in the text.
After the revival of art, the study of Archimedes theory revived, and many pioneers emerged.
Who?
The real foundation of calculus is in
17
Century,
Starting with Descartes' analytic geometry,
receive
The masterpiece is the creation of calculus, which brings the history of mathematics into a new period-variable mathematics.
Period. Euclidean geometry and algebra in ancient and medieval times were constants.
Mathematics and calculus are real variable mathematics and a great revolution in mathematics. Calculus in mathematics
This can be regarded as a great achievement in the history of development, because the establishment of calculus not only solved
At that time, some important scientific problems and some important branches of mathematics were produced from this.
Such as differential equation, infinite series, differential geometry, variational method, complex variable function, etc.
Calculus has solved some important problems: ① finding instantaneous velocity; ② finding tangent of curve; ③ finding.
The maximum value ④ of the function is to find the curve length. These problems are very important for the development of astronomy, physics and other disciplines.
An important promoting role. Because it is important, it is also difficult to learn, and it is a freshman science.
The main math problems that make students have a headache.
Preview is very important. Preview is not self-study, but browsing for books.
Key and difficult points, in order to "concentrate on class"
.
If you don't have much time, you can browse one
Have a general impression of the main content that the teacher will talk about, which can be to some extent
To some extent, it helps you keep up with the teacher's thoughts in class. If you have enough time, you can keep up with the teacher's ideas.
In addition to browsing, you can also read some contents in detail and prepare questions.
What's the difference between your own understanding and the teacher's explanation?
What problems need to be discussed with the teacher?
If you can do this, then your study will become more active and in-depth and you will achieve something.
Better results. Don't rush to do the problem, think deeply about the textbook first. Do the problem
Don't turn over the answer easily, think it over and discuss it with your classmates. Do the questions or not?
Coming out is more rewarding than doing it. Confidence in learning is also very important. Improve confidence, cultivate
Good psychological quality and courage to overcome all kinds of difficulties; Don't let it go just because you're not interested at the moment.
Abandon,
Interest is not innate,
It is cultivated slowly the day after tomorrow.
Good study tradition,
It is the quality that contemporary college students should have to work hard to realize the glory of their lives.
In class, we should focus on the difficulties in preview and give guidance to teachers for the key difficulties.
After asking questions, the teacher expects the students to "interrupt" his lecture in the university class, teacher.
I also hope that I can exchange and discuss classroom knowledge with students, so that classroom questions can not only get the special attention of teachers.
The explanation can also be on the topic. Dare to ask questions in class. In class, if you have any questions.
Ask, you should ask right away. Because of your question, there may be situations where other students are afraid to ask.
Problems; It could be everyone here.
(
Including teachers.
)
Problems that have not been considered.
Asking questions in class is of great help not only to yourself but also to the whole class. Lively students
A dynamic learning environment is not only created by teachers, but also requires the participation of students and teachers.
Students all hope and attach great importance to students' more positive performance in class. Believe this.
Interactive learning process will definitely make you gain more in the process of learning calculus.
There are many integral formulas in calculus learning, so we must remember and skillfully use some integrals.
Formulas can shorten the time of doing problems, which is of great help to future study, while integral formulas
Many and complex, need special memory. Deducing the formula many times improves the understanding of the formula.
It is also a clever use of other formulas in disguise, and the derivation of formulas in mathematics learning needs other formulas.
With the help of, the basic integral formula has the advantages of complex integral formula. & gt
Question 10: How to learn calculus well? I am a business major, and I am good at calculus. My teacher writes on the blackboard in class, so I think your teacher should write too. I think you should take notes, which is especially useful. Never read a book when reviewing. I understand the example given by the teacher. I am doing the problem. Frankly speaking, my textbook is different from yours, and I believe the method is equally applicable. When I help others to review mathematics, I also do examples and do related homework, which has a particularly good effect. If you can do the problems in the book yourself and read the counseling book later, don't be in a hurry! The various types of limit calculation and integral must be understood, which is the basis of general books (integral and differential are the operations of derivative and reciprocal). Do exercises repeatedly after class, and pay attention to induction in class. For example, in the chapter of infinite series, there is a comparative judgment method to judge the convergence and divergence of positive series. The book talks a lot, in fact, it is summed up in eight words, "big harvest and small harvest, small hair and great hair", which is particularly convenient when reviewing. Don't be discouraged because you have no foundation. Are "irrelevant variables". Proceed from the limit and wish you success. If you have questions, you can post them!